CUET PG 2022 — Mathematics PYQ

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Question

CUET PG 2022 — Mathematics PYQ

CUET PG | Mathematics | 2022

If $(25)^{7.5} \times (5)^{2.5} \div (125)^{1.5} = (5)^{x}$ then $x = ?$

Choose the correct answer:

Explanation

1. Express all bases as powers of 5:

$25 = 5^2$
$125 = 5^3$

2. Substitute these values back into the equation:

(5^2)^{7.5} \times (5)^{2.5} \div (5^3)^{1.5} = 5^x

3. Apply the Power of a Power rule $(a^m)^n = a^{m \times n}$ :

(5)^{2 \times 7.5} \times (5)^{2.5} \div (5)^{3 \times 1.5} = 5^x

(5)^{15} \times (5)^{2.5} \div (5)^{4.5} = 5^x

4. Apply Exponent Rules for Multiplication and Division:

Multiplication: $a^m \times a^n = a^{m+n}$
Division: $a^m \div a^n = a^{m-n}$

5^{15 + 2.5 - 4.5} = 5^x

5. Simplify the exponents:

5^{17.5 - 4.5} = 5^x

5^{13} = 5^x

x = 13