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lions [1.4K]
3 years ago
7

Which is the value of this expression when p=-2 and q=-1?

Mathematics
1 answer:
saul85 [17]3 years ago
8 0

Answer:

D. 4

Step-by-step explanation:

[(p^2) (q^{-3}) ]^{-2}.[(p)^{-3}(q)^5] ^{-2}\\\\=[(p^2) (q^{-3}) \times(p)^{-3}(q)^5 ]^{-2}\\\\=[(p^{2}) \times(p)^{-3} \times (q^{-3}) \times(q)^5 ]^{-2}\\\\=[(p^{2-3}) \times (q^{5-3}) ]^{-2}\\\\=[(p^{-1}) \times (q^{2}) ]^{-2}\\\\=(p^{-1\times (-2)}) \times (q^{2\times (-2) }) \\\\=p^{2}\times q^{-4} \\\\= \frac{p^2}{q^4}\\\\= \frac{(-2)^2}{(-1)^4}\\\\= \frac{4}{1}\\\\= 4

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5 0
3 years ago
Read 2 more answers
(-2/3)^7*(3/5)^6*(5/6)^5*(1/3)^-7 simplify of law of indices ​
Wewaii [24]

Answer:

\boxed {-\frac{12}{5}}

Step-by-step explanation:

Solve the following expression:

(-\frac{2}{3})^{7} \times (\frac{3}{5})^{6} \times (\frac{5}{6})^{5} \times (\frac{1}{3})^{-7}

-Calculate -\frac{2}{3} to the power of 7:

(-\frac{2}{3})^{7} \times (\frac{3}{5})^{6} \times (\frac{5}{6})^{5} \times (\frac{1}{3})^{-7}

-\frac{128}{2187} \times (\frac{3}{5})^{6} \times (\frac{5}{6})^{5} \times (\frac{1}{3})^{-7}

-Calculate \frac{3}{5} to the power of 6:

-\frac{128}{2187} \times (\frac{3}{5})^{6} \times (\frac{5}{6})^{5} \times (\frac{1}{3})^{-7}

-\frac{128}{2187} \times (\frac{729}{15625}) \times (\frac{5}{6})^{5} \times (\frac{1}{3})^{-7}

-Multiply both -\frac{128}{2187} and \frac{729}{15625}:

-\frac{128}{2187} \times (\frac{729}{15625}) \times (\frac{5}{6})^{5} \times (\frac{1}{3})^{-7}

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-Calculate \frac{5}{6} to the power of 5:

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-\frac{128}{46875} \times (\frac{3125}{7776}) \times (\frac{1}{3})^{-7}

-Multiply both -\frac{128}{46875} and \frac{3125}{7776}:

-\frac{128}{46875} \times (\frac{3125}{7776}) \times (\frac{1}{3})^{-7}

-\frac{4}{3645} \times (\frac{1}{3})^{-7}

-Calculate \frac{1}{3} to the power of -7:

-\frac{4}{3645} \times (\frac{1}{3})^{-7}

-\frac{4}{3645} \times 2181

-Multiply both the -\frac{4}{3645} and 2187:

-\frac{4}{3645} \times 2181

\boxed {-\frac{12}{5}}

Therefore, the final answer is -\frac{12}{5}.

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