Question

Which expression is equivalent to the quantity seven raised to the negative second power times three raised to the fifth power end quantity all raised to the negative second power?

a) seven raised to the fourth power divided by three raised to the tenth power

b) negative seven raised to the fourth power divided by three raised to the tenth power

c) three raised to the third power divided by seven raised to the fourth power

d) negative three raised to the third power divided by seven raised to the fourth power

Answer 1

To simplify the expression, we start by raising $7^{-2} \cdot 3^5$ to the $-2$nd power. We have $(7^{-2} \cdot 3^5)^{-2} = 7^{-2\cdot -2} \cdot 3^{5 \cdot -2} = 7^{4} \cdot 3^{-10} = \frac{7^4}{3^{10}}$. Thus, the answer is $\boxed{\textbf{(a)}\ seven\,\mathrm{raised\,to\,the\,fourth\,power\,divided\,by\,three\,\mathrm{raised\,to\,the}\,tenth\,\mathrm{power}}}$.