Solve [(- x)/Y] * X * [(- x)/Y) ^ 14 | 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

$$[\frac{-x}{Y}]X[\frac{-x}{Y})^{14}$$

Evaluate

$\frac{x^{6}}{y^{5}}$

Short Solution Steps

To raise $\frac{-x}{y}$ to a power, raise both numerator and denominator to the power and then divide.

$$\frac{x}{y}x\times \frac{\left(-x\right)^{4}}{y^{4}}$$

Express $\frac{x}{y}x$ as a single fraction.

$$\frac{xx}{y}\times \frac{\left(-x\right)^{4}}{y^{4}}$$

Multiply $\frac{xx}{y}$ times $\frac{\left(-x\right)^{4}}{y^{4}}$ by multiplying numerator times numerator and denominator times denominator.

$$\frac{xx\left(-x\right)^{4}}{yy^{4}}$$

Multiply $x$ and $x$ to get $x^{2}$.

$$\frac{x^{2}\left(-x\right)^{4}}{yy^{4}}$$

To multiply powers of the same base, add their exponents. Add $1$ and $4$ to get $5$.

$$\frac{x^{2}\left(-x\right)^{4}}{y^{5}}$$

Expand $\left(-x\right)^{4}$.

$$\frac{x^{2}\left(-1\right)^{4}x^{4}}{y^{5}}$$

Calculate $-1$ to the power of $4$ and get $1$.

$$\frac{x^{2}\times 1x^{4}}{y^{5}}$$

To multiply powers of the same base, add their exponents. Add $2$ and $4$ to get $6$.

$$\frac{x^{6}\times 1}{y^{5}}$$

For any term $t$, $t\times 1=t$ and $1t=t$.

$$\frac{x^{6}}{y^{5}}$$

Expand

$\frac{x^{6}}{y^{5}}$

Short Solution Steps

To raise $\frac{-x}{y}$ to a power, raise both numerator and denominator to the power and then divide.

$$\frac{x}{y}x\times \frac{\left(-x\right)^{4}}{y^{4}}$$

Express $\frac{x}{y}x$ as a single fraction.

$$\frac{xx}{y}\times \frac{\left(-x\right)^{4}}{y^{4}}$$

Multiply $\frac{xx}{y}$ times $\frac{\left(-x\right)^{4}}{y^{4}}$ by multiplying numerator times numerator and denominator times denominator.

$$\frac{xx\left(-x\right)^{4}}{yy^{4}}$$

Multiply $x$ and $x$ to get $x^{2}$.

$$\frac{x^{2}\left(-x\right)^{4}}{yy^{4}}$$

To multiply powers of the same base, add their exponents. Add $1$ and $4$ to get $5$.

$$\frac{x^{2}\left(-x\right)^{4}}{y^{5}}$$

Expand $\left(-x\right)^{4}$.

$$\frac{x^{2}\left(-1\right)^{4}x^{4}}{y^{5}}$$

Calculate $-1$ to the power of $4$ and get $1$.

$$\frac{x^{2}\times 1x^{4}}{y^{5}}$$

To multiply powers of the same base, add their exponents. Add $2$ and $4$ to get $6$.

$$\frac{x^{6}\times 1}{y^{5}}$$

For any term $t$, $t\times 1=t$ and $1t=t$.

$$\frac{x^{6}}{y^{5}}$$