Question

a)5¹²×5¹³= b)7⁵×7²×7= c)12¹⁴÷12⁸×12²=​

Answer 1

Potência de potência:

$\large\begin{array}{lr}\sf (a^{a})^{b} = a^{a\times b}\end{array}$

Multiplicação de potências com bases iguais:

$\large\begin{array}{lr}\sf a^{b} \cdot a^{c}= a^{b+c}\end{array}$

Divisão de potências com bases iguais:

$\large\begin{array}{lr}\sf \frac{a^{b}}{a^{c}} = a^{b-c}\end{array}$

a)

$\large\begin{array}{lr}\sf 5^{12} \times 5^{13}\\\\\sf 5^{12 +15}\\\\\sf = \underline{\boxed{\red{\sf 5^{25}}}}\end{array}$

b)

$\large\begin{array}{lr}\sf 7^{5} \times 7^{2} \times 7\\\\\sf 7^{5+2+1}\\\\\sf = \underline{\boxed{\red{\sf 7^{8}}}}\end{array}$

c)

$\large\begin{array}{lr}\sf 12^{14} \div 12^{8} \times 12^{12}\\\\\sf 12^{14-8} \times 12^{12}\ \\\\\sf 12^{6} \times 12^{12}\\\\\sf =\underline{\boxed{\red{\sf 12^{18}}}}\end{array}$

Espero ter ajudado.

Bons estudos.

• Att. FireClassis.