Question

simplify and express each of the following in exponential form using laws of exponents. 5 ¹² ÷ 5⁴​

Answer 1

Answer:

5¹⁶

Step-by-step explanation:

5⁴×5¹²

5⁴+¹²

5¹⁶

Answer 2

Algebra - Exponents

The following quotient law of exponents will be used to find the solution:

$\boxed{x^m \div x^n = x^{m - n}}$

Where, m and n are numbers respectively.

According to the quotient law of exponents, we can divide two numbers with the same base by subtracting the exponents.

We know that,

$\implies \boxed{x^m \div x^n = x^{m - n}}$

Therefore,

$\implies 5^{12} \div 5^4 \\ \\ \implies 5^{12-4} \\ \\ \implies 5^8 \\ \\ \implies \boxed{390625}$

Hence, the answer is 390625.

$\rule{90mm}{2pt}$

MORE TO KNOW

$\boxed{\begin{array}{l}\bf{\dag}\:\:\underline{\textsf{\textbf{Law of Exponents :}}}\\\\\bigstar\:\:\sf\dfrac{a^m}{a^n} = a^{m - n}\\\\\bigstar\:\:\sf{(a^m)^n = a^{mn}}\\\\\bigstar\:\:\sf(a^m)(a^n) = a^{m + n}\\\\\bigstar\:\:\sf\dfrac{1}{a^n} = a^{-n}\\\\\bigstar\:\:\sf\sqrt[\sf n]{\sf a} = (a)^{\frac{1}{n}}\end{array}}$