Simplify. Express Your Answer Using Positive Exponents. ( 2 R 2 S T ) ( 5 R 9 S 5 T ) ( 7 R 7 S T 7 (2r^2st)(5r^9s^5t)(7r^7st^7 ( 2 R 2 S T ) ( 5 R 9 S 5 T ) ( 7 R 7 S T 7 ]

Simplify. Express your answer using positive exponents. $(2r^2st)(5r^9s^5t)(7r^7st^7)$

Understanding the Problem

The given problem involves simplifying the expression $(2r^2st)(5r^9s^5t)(7r^7st^7)$ using positive exponents. To simplify this expression, we need to apply the rules of exponents and multiplication of variables.

Applying the Rules of Exponents

When multiplying variables with the same base, we add the exponents. However, when multiplying variables with different bases, we multiply the variables and keep the exponents as they are. In this case, we have variables with the same base ($r$, $s$, and $t$) and different exponents.

Simplifying the Expression

To simplify the expression, we can start by multiplying the coefficients (the numbers in front of the variables) and then multiply the variables with the same base.

Multiplying the Coefficients

The coefficients are 2, 5, and 7. We multiply these numbers together to get:

2 × 5 × 7 = 70

Multiplying the Variables

Now, we multiply the variables with the same base. We have three variables: $r$, $s$, and $t$. We multiply these variables with their respective exponents:

$r^2 \times r^9 \times r^7 = r^{2+9+7} = r^{18}$

$s \times s^5 \times s = s^{1+5+1} = s^7$

$t \times t^7 \times t = t^{1+7+1} = t^9$

Combining the Results

Now, we combine the results of multiplying the coefficients and the variables:

70 × $r^{18}$ × $s^7$ × $t^9$

Expressing the Answer Using Positive Exponents

The final answer is:

70$r^{18}s^7t^9$

This is the simplified expression using positive exponents.

Conclusion

In this article, we simplified the expression $(2r^2st)(5r^9s^5t)(7r^7st^7)$ using positive exponents. We applied the rules of exponents and multiplication of variables to simplify the expression. The final answer is 70$r^{18}s^7t^9$.
Simplify. Express your answer using positive exponents. $(2r^2st)(5r^9s^5t)(7r^7st^7)$

Understanding the Problem

The given problem involves simplifying the expression $(2r^2st)(5r^9s^5t)(7r^7st^7)$ using positive exponents. To simplify this expression, we need to apply the rules of exponents and multiplication of variables.

Applying the Rules of Exponents

When multiplying variables with the same base, we add the exponents. However, when multiplying variables with different bases, we multiply the variables and keep the exponents as they are. In this case, we have variables with the same base ($r$, $s$, and $t$) and different exponents.

Simplifying the Expression

To simplify the expression, we can start by multiplying the coefficients (the numbers in front of the variables) and then multiply the variables with the same base.

Multiplying the Coefficients

The coefficients are 2, 5, and 7. We multiply these numbers together to get:

2 × 5 × 7 = 70

Multiplying the Variables

Now, we multiply the variables with the same base. We have three variables: $r$, $s$, and $t$. We multiply these variables with their respective exponents:

$r^2 \times r^9 \times r^7 = r^{2+9+7} = r^{18}$

$s \times s^5 \times s = s^{1+5+1} = s^7$

$t \times t^7 \times t = t^{1+7+1} = t^9$

Combining the Results

Now, we combine the results of multiplying the coefficients and the variables:

70 × $r^{18}$ × $s^7$ × $t^9$

Expressing the Answer Using Positive Exponents

The final answer is:

70$r^{18}s^7t^9$

This is the simplified expression using positive exponents.

Q&A

Q: What are the rules of exponents?

A: The rules of exponents state that when multiplying variables with the same base, we add the exponents. However, when multiplying variables with different bases, we multiply the variables and keep the exponents as they are.

Q: How do we simplify the expression $(2r^2st)(5r^9s^5t)(7r^7st^7)$?

A: To simplify the expression, we multiply the coefficients (the numbers in front of the variables) and then multiply the variables with the same base.

Q: What is the coefficient of the simplified expression?

A: The coefficient of the simplified expression is 70.

Q: What are the exponents of the variables in the simplified expression?

A: The exponents of the variables in the simplified expression are $r^{18}$, $s^7$, and $t^9$.

Q: How do we express the answer using positive exponents?

A: To express the answer using positive exponents, we keep the exponents as they are and do not change the sign of the exponents.

Q: What is the final answer?

A: The final answer is 70$r^{18}s^7t^9$.

Conclusion

In this article, we simplified the expression $(2r^2st)(5r^9s^5t)(7r^7st^7)$ using positive exponents. We applied the rules of exponents and multiplication of variables to simplify the expression. The final answer is 70$r^{18}s^7t^9$.