Solve 16x ^ 5 - 4 ^ - 2 * x ^ 3 * (2x ^ 2) ^ - 3 | Equatix - Math Solver

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Example

3(r+2s)=2t-4

a⋅(b-2)=3b

3(r+2s)=2t-4

a⋅(b-2)=3b

Question

$$16x^{5}-4^{-2}x^{3}\times(2x^{2})^{-3}$$

Evaluate

$16x^{5}-\frac{1}{128x^{3}}$

Solution Steps

Calculate $4$ to the power of $-2$ and get $\frac{1}{16}$.

$$16x^{5}-\frac{1}{16}x^{3}\times \left(2x^{2}\right)^{-3}$$

Expand $\left(2x^{2}\right)^{-3}$.

$$16x^{5}-\frac{1}{16}x^{3}\times 2^{-3}\left(x^{2}\right)^{-3}$$

To raise a power to another power, multiply the exponents. Multiply $2$ and $-3$ to get $-6$.

$$16x^{5}-\frac{1}{16}x^{3}\times 2^{-3}x^{-6}$$

Calculate $2$ to the power of $-3$ and get $\frac{1}{8}$.

$$16x^{5}-\frac{1}{16}x^{3}\times \frac{1}{8}x^{-6}$$

Multiply $\frac{1}{16}$ and $\frac{1}{8}$ to get $\frac{1}{128}$.

$$16x^{5}-\frac{1}{128}x^{3}x^{-6}$$

To multiply powers of the same base, add their exponents. Add $3$ and $-6$ to get $-3$.

$$16x^{5}-\frac{1}{128}x^{-3}$$

Expand

$16x^{5}-\frac{1}{128x^{3}}$

Solution Steps

Calculate $4$ to the power of $-2$ and get $\frac{1}{16}$.

$$16x^{5}-\frac{1}{16}x^{3}\times \left(2x^{2}\right)^{-3}$$

Expand $\left(2x^{2}\right)^{-3}$.

$$16x^{5}-\frac{1}{16}x^{3}\times 2^{-3}\left(x^{2}\right)^{-3}$$

To raise a power to another power, multiply the exponents. Multiply $2$ and $-3$ to get $-6$.

$$16x^{5}-\frac{1}{16}x^{3}\times 2^{-3}x^{-6}$$

Calculate $2$ to the power of $-3$ and get $\frac{1}{8}$.

$$16x^{5}-\frac{1}{16}x^{3}\times \frac{1}{8}x^{-6}$$

Multiply $\frac{1}{16}$ and $\frac{1}{8}$ to get $\frac{1}{128}$.

$$16x^{5}-\frac{1}{128}x^{3}x^{-6}$$

To multiply powers of the same base, add their exponents. Add $3$ and $-6$ to get $-3$.

$$16x^{5}-\frac{1}{128}x^{-3}$$