Simplify (2r^-5yz^-4)(2r)^-5

$(2 r^{- 5} y z^{- 4}) {(2 r)}^{- 5}$

Step 1

Rewrite the expression using the negative exponent rule

$b^{- n} = \frac{1}{b^{n}}$ .

$2 \frac{1}{r^{5}} y z^{- 4} {(2 r)}^{- 5}$

Step 2

Combine

$2$ and

$\frac{1}{r^{5}}$ .

$\frac{2}{r^{5}} y z^{- 4} {(2 r)}^{- 5}$

Step 3

Combine

$\frac{2}{r^{5}}$ and

$y$ .

$\frac{2 y}{r^{5}} z^{- 4} {(2 r)}^{- 5}$

Step 4

Rewrite the expression using the negative exponent rule

$b^{- n} = \frac{1}{b^{n}}$ .

$\frac{2 y}{r^{5}} \cdot \frac{1}{z^{4}} {(2 r)}^{- 5}$

Step 5

Combine.

$\frac{2 y \cdot 1}{r^{5} z^{4}} {(2 r)}^{- 5}$

Step 6

Multiply

$2$ by

$1$ .

$\frac{2 y}{r^{5} z^{4}} {(2 r)}^{- 5}$

Step 7

Rewrite the expression using the negative exponent rule

$b^{- n} = \frac{1}{b^{n}}$ .

$\frac{2 y}{r^{5} z^{4}} \cdot \frac{1}{{(2 r)}^{5}}$

Step 8

Combine fractions.

Combine.

$\frac{2 y \cdot 1}{r^{5} z^{4} {(2 r)}^{5}}$

Multiply

$2$ by

$1$ .

$\frac{2 y}{r^{5} z^{4} {(2 r)}^{5}}$

Step 9

Simplify the denominator.

Apply the product rule to

$2 r$ .

$\frac{2 y}{r^{5} z^{4} \cdot 2^{5} r^{5}}$

Multiply

$r^{5}$ by

$r^{5}$ by adding the exponents.

Move

$r^{5}$ .

$\frac{2 y}{r^{5} r^{5} z^{4} \cdot 2^{5}}$

Use the power rule

$a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{2 y}{r^{5 + 5} z^{4} \cdot 2^{5}}$

Add

$5$ and

$5$ .

$\frac{2 y}{r^{10} z^{4} \cdot 2^{5}}$

Raise

$2$ to the power of

$5$ .

$\frac{2 y}{r^{10} z^{4} \cdot 32}$

Step 10

Reduce the expression by cancelling the common factors.

Cancel the common factor of

$2$ and

$32$ .

Factor

$2$ out of

$2 y$ .

$\frac{2 (y)}{r^{10} z^{4} \cdot 32}$

Cancel the common factors.

Factor

$2$ out of

$r^{10} z^{4} \cdot 32$ .

$\frac{2 (y)}{2 (r^{10} z^{4} \cdot 16)}$

Cancel the common factor.

$\frac{2 y}{2 (r^{10} z^{4} \cdot 16)}$

Rewrite the expression.

$\frac{y}{r^{10} z^{4} \cdot 16}$

Move

$16$ to the left of

$r^{10} z^{4}$ .

$\frac{y}{16 r^{10} z^{4}}$

Simplify (2r^-5yz^-4)(2r)^-5

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