Solve C. - (a ^ - 3 * b ^ 10 * c ^ 8 * b * c ^ 8)/((b ^ - 10 * c ^ 6) ^ 4) | 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

$$- \frac { a ^ { - 3 } b ^ { 10 } c ^ { 8 } \times b c ^ { 8 } } { ( b ^ { - 10 } \times c ^ { 6 } ) ^ { 4 } }$$

Evaluate

$-\frac{b^{51}}{a^{3}c^{8}}$

Solution Steps

To multiply powers of the same base, add their exponents. Add $10$ and $1$ to get $11$.

$$-\frac{a^{-3}b^{11}c^{8}c^{8}}{\left(b^{-10}c^{6}\right)^{4}}$$

To multiply powers of the same base, add their exponents. Add $8$ and $8$ to get $16$.

$$-\frac{a^{-3}b^{11}c^{16}}{\left(b^{-10}c^{6}\right)^{4}}$$

Expand $\left(b^{-10}c^{6}\right)^{4}$.

$$-\frac{a^{-3}b^{11}c^{16}}{\left(b^{-10}\right)^{4}\left(c^{6}\right)^{4}}$$

To raise a power to another power, multiply the exponents. Multiply $-10$ and $4$ to get $-40$.

$$-\frac{a^{-3}b^{11}c^{16}}{b^{-40}\left(c^{6}\right)^{4}}$$

To raise a power to another power, multiply the exponents. Multiply $6$ and $4$ to get $24$.

$$-\frac{a^{-3}b^{11}c^{16}}{b^{-40}c^{24}}$$

Cancel out $c^{16}$ in both numerator and denominator.

$$-\frac{a^{-3}b^{11}}{b^{-40}c^{8}}$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent.

$$-\frac{a^{-3}b^{51}}{c^{8}}$$

Expand

$-\frac{b^{51}}{a^{3}c^{8}}$

Solution Steps

To multiply powers of the same base, add their exponents. Add $10$ and $1$ to get $11$.

$$-\frac{a^{-3}b^{11}c^{8}c^{8}}{\left(b^{-10}c^{6}\right)^{4}}$$

To multiply powers of the same base, add their exponents. Add $8$ and $8$ to get $16$.

$$-\frac{a^{-3}b^{11}c^{16}}{\left(b^{-10}c^{6}\right)^{4}}$$

Expand $\left(b^{-10}c^{6}\right)^{4}$.

$$-\frac{a^{-3}b^{11}c^{16}}{\left(b^{-10}\right)^{4}\left(c^{6}\right)^{4}}$$

To raise a power to another power, multiply the exponents. Multiply $-10$ and $4$ to get $-40$.

$$-\frac{a^{-3}b^{11}c^{16}}{b^{-40}\left(c^{6}\right)^{4}}$$

To raise a power to another power, multiply the exponents. Multiply $6$ and $4$ to get $24$.

$$-\frac{a^{-3}b^{11}c^{16}}{b^{-40}c^{24}}$$

Cancel out $c^{16}$ in both numerator and denominator.

$$-\frac{a^{-3}b^{11}}{b^{-40}c^{8}}$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent.

$$-\frac{a^{-3}b^{51}}{c^{8}}$$