Problem 110 Simplify each exponential expres... [FREE SOLUTION]

Chapter 0: Problem 110

Simplify each exponential expression. Assume that variables represent nonzero real numbers. $$\left(3 x^{-4} y z^{-7}\right)(3 x)^{-3}$$

Short Answer

Expert verified

The simplified exponential expression form is $3^2 y x^{-7} z^{-7}$.

Step by step solution

Rewrite the exponential multiplication

Rewrite $\left(3 x^{-4} y z^{-7}\right)(3 x)^{-3}$ as $(3 x^{-4} y z^{-7})(3 x^{-3})$. Observe that it鈥檚 multiplying like bases 鈥� in this case, the base is $x$. Follow the rule of multiplying bases by adding the exponents.

Multiply the like bases

So now the expression becomes $(3 y z^{-7} x^{-4})(1 x^{-3})$. The coefficient of $x^{-3}$ in the second parentheses is one since there is no number before it. Use the multiplication rule of exponents to add the powers of $x$. This rule is $x^m x^n = x^{m+n}$. Therefore, the powers of $x$ can be simplified as $x^{-4}x^{-3}=x^{-4-3}=x^{-7}$

FInal expression

Substituting everything into the expression, the final simplified form is $3^2 y x^{-7} z^{-7}$. Notice that $3^2$ is a result of $(3)$ times $(3)$. This is because both were part of the original functions, and now they are multiplied together.

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91影视

Simplify each exponential expression. Assume that variables represent nonzero real numbers. $$\left(3 x^{-4} y z^{-7}\right)(3 x)^{-3}$$

Short Answer

Step by step solution

Rewrite the exponential multiplication

Multiply the like bases

FInal expression

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