Solve (-7/11)^13*(-7/11)^8=(-7/11)^13

$$( \frac { - 7 } { 11 } ) ^ { 13 } \times ( \frac { - 7 } { 11 } ) ^ { 8 } = ( \frac { - 7 } { 11 } ) ^ { 13 }$$

Verify

Solution Steps

To multiply powers of the same base, add their exponents. Add 13 and 8 to get 21.

$$\left(\frac{-7}{11}\right)^{21}=\left(\frac{-7}{11}\right)^{13}$$

Fraction \frac{-7}{11} can be rewritten as -\frac{7}{11} by extracting the negative sign.

$$\left(-\frac{7}{11}\right)^{21}=\left(\frac{-7}{11}\right)^{13}$$

Calculate -\frac{7}{11} to the power of 21 and get -\frac{558545864083284007}{7400249944258160101211}.

$$-\frac{558545864083284007}{7400249944258160101211}=\left(\frac{-7}{11}\right)^{13}$$

Fraction \frac{-7}{11} can be rewritten as -\frac{7}{11} by extracting the negative sign.

$$-\frac{558545864083284007}{7400249944258160101211}=\left(-\frac{7}{11}\right)^{13}$$

Calculate -\frac{7}{11} to the power of 13 and get -\frac{96889010407}{34522712143931}.

$$-\frac{558545864083284007}{7400249944258160101211}=-\frac{96889010407}{34522712143931}$$

Least common multiple of 7400249944258160101211 and 34522712143931 is 7400249944258160101211. Convert -\frac{558545864083284007}{7400249944258160101211} and -\frac{96889010407}{34522712143931} to fractions with denominator 7400249944258160101211.

$$-\frac{558545864083284007}{7400249944258160101211}=-\frac{20769019852041874567}{7400249944258160101211}$$

Compare -\frac{558545864083284007}{7400249944258160101211} and -\frac{20769019852041874567}{7400249944258160101211}.

$$\text{false}$$