Question

Find the value of ${[15625\times (-729)]}^{\frac{1}{3}}$

• A. $225$
• B. $-225$
• C. $-252$
• D. $-522$

Answer 1

The correct option is B $-225$

We know $15625=5^6$, $729=3^6$

Therefore, $(15625\times (-729){)}^{1/3}=(5^6\times 3^6{)}^{1/3}\times (-1{)}^{1/3}$

$=5^2\times 3^2\times (-1{)}^{1/3}$

$=25\times 9\times (-1{)}^{1/3}$

$=225\times (-1{)}^{1/3}$

$=-225$ (one of the cube roots of $-1$ is $-1$)