Question

Write the proper numbers in the boxes.

(1) $3^{10}÷3^6=3^{\boxed{}-\boxed{}}$
(2) $7^{19}÷7^4=7^{\boxed{}}$
(3) ${\left(\frac{1}{2}\right)}^{20}÷{\left(\frac{1}{2}\right)}^{12}={\left(\frac{1}{2}\right)}^{\boxed{}}$
(4) ${\left(2.1\right)}^{15}÷{\left(2.1\right)}^{13}={\left(2.1\right)}^{\boxed{}}$
(5) $x^{14}÷x^{10}=x^{\boxed{}}$
(6) $x^6÷x^4=x^{\boxed{}}$

Answer 1

(1) $3^{10}÷3^6=3^{\boxed{}-\boxed{}}$
Consider 3¹⁰ ÷ 3⁶
$=3^{\boxed{10}-\boxed{6}}\left(a^m÷a^n=a^{m-n}\mathrm{when}m>n\right)$

(2) $7^{19}÷7^4=7^{\boxed{}}$
Consider 7¹⁹ ÷ 7⁴ (a^m ÷ aⁿ = a^m–n when m > n)
$=7^{\boxed{15}}$

(3) ${\left(\frac{1}{2}\right)}^{20}÷{\left(\frac{1}{2}\right)}^{12}={\left(\frac{1}{2}\right)}^{\boxed{}}$
Consider ${\left(\frac{1}{2}\right)}^{20}÷{\left(\frac{1}{2}\right)}^{12}$
$$\begin{gathered} ={\left(\frac{1}{2}\right)}^{20-12}\left(a^m÷a^n=a^{m-n}\mathrm{when}m>n\right) \\ ={\left(\frac{1}{2}\right)}^{\boxed{8}} \end{gathered}$$

(4) ${\left(2.1\right)}^{15}÷{\left(2.1\right)}^{13}={\left(2.1\right)}^{\boxed{}}$
Consider (2.1)¹⁵ ÷ (2.1)¹³
= (2.1)^15–13 (a^m ÷ aⁿ = a^m–n when m > n)
$={\left(2.1\right)}^{\boxed{2}}$

(5) $x^{14}÷x^{10}=x^{\boxed{}}$
Consider x¹⁴ ÷ x¹⁰
= x^14–10 (a^m ÷ aⁿ = a^m–n when m > n)
$=x^{\boxed{4}}$

(6) $x^6÷x^4=x^{\boxed{}}$
Consider x⁶ ÷ x⁴
= x^6–4 (a^m ÷ aⁿ = a^m–n when m > n)
$=x^{\boxed{2}}$