Question

Write the proper numbers in the boxes.

(1) ${\left(5\times 8\right)}^2=5^{\boxed{}}\times 8^{\boxed{}}$
(2) ${\left[\left(\frac{3}{7}\right)\times \left(\frac{7}{9}\right)\right]}^3={\left(\frac{3}{7}\right)}^{\boxed{}}\times {\left(\frac{7}{9}\right)}^{\boxed{}}$
(3) ${\left[\left(\frac{-2}{3}\right)\times \left(\frac{-5}{11}\right)\right]}^4={\left(\frac{-2}{3}\right)}^{\boxed{}}\times {\left(\frac{-5}{11}\right)}^{\boxed{}}$
(4) ${\left(xy\right)}^{10}=x^{\boxed{}}\times y^{\boxed{}}$
(5) ${\left(pq\right)}^4=p^{\boxed{}}\times q^{\boxed{}}$

Answer 1

(1) ${\left(5\times 8\right)}^2=5^{\boxed{}}\times 8^{\boxed{}}$
Consider (5 × 8)²
$=5^{\boxed{2}}\times 8^{\boxed{2}}\left[{\left(a\times b\right)}^m=a^m\times b^m\right]$

(2) ${\left[\left(\frac{3}{7}\right)\times \left(\frac{7}{9}\right)\right]}^3={\left(\frac{3}{7}\right)}^{\boxed{}}\times {\left(\frac{7}{9}\right)}^{\boxed{}}$
Consider ${\left[\left(\frac{3}{7}\right)\times \left(\frac{7}{9}\right)\right]}^3$
$={\left(\frac{3}{7}\right)}^{\boxed{3}}\times {\left(\frac{7}{9}\right)}^{\boxed{3}}\left[{\left(a\times b\right)}^m=a^m\times b^m\right]$

(3) ${\left[\left(\frac{-2}{3}\right)\times \left(\frac{-5}{11}\right)\right]}^4={\left(\frac{-2}{3}\right)}^{\boxed{}}\times {\left(\frac{-5}{11}\right)}^{\boxed{}}$
Consider ${\left[\left(\frac{-2}{3}\right)\times \left(\frac{-5}{11}\right)\right]}^4$
$={\left(\frac{-2}{3}\right)}^{\boxed{4}}\times {\left(\frac{-5}{11}\right)}^{\boxed{4}}\left[{\left(a\times b\right)}^m=a^m\times b^m\right]$

(4) ${\left(xy\right)}^{\boxed{10}}=x^{\boxed{}}\times y^{\boxed{}}$
Consider (xy)¹⁰
$=x^{\boxed{10}}\times y^{\boxed{10}}\left[{\left(a\times b\right)}^m=a^m\times b^m\right]$

(5) ${\left(pq\right)}^4=p^{\boxed{}}\times q^{\boxed{}}$
Consider (pq)⁴
$=p^{\boxed{4}}\times q^{\boxed{4}}\left[{\left(a\times b\right)}^m=a^m\times b^m\right]$