Fractions and Decimals

Discrete Mathematics

Differential Equations

Solved on Sep 18, 2023

Calculate the value of $x$ in the equation $19^{15} \div 19^{3} = 19^{x}$ .

STEP 1

Assumptions1. The base of all the exponents is19. . The operation involved is division.
3. The laws of exponents apply.

STEP 2

According to the laws of exponents, when we divide two numbers with the same base, we subtract the exponent of the denominator from the exponent of the numerator. $a^{m} \div a^{n} = a^{m-n}$

STEP 3

Now, apply this rule to the given problem. $19^{15} \div19^{3} =19^{15-3}$

STEP 4

Subtract the exponents.
$19^{15-3} =19^{12}$ Therefore, the value of $x$ is12.

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