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

Related Questions