Math  /  Algebra

QuestionSimplify the expression completely: 5x18y2037x5y7\frac{5 x^{18} y^{20}}{37 x^{5} y^{7}}
Answer = \square

Studdy Solution

STEP 1

1. The expression is a fraction involving exponents.
2. Simplification involves reducing the expression by canceling common factors in the numerator and the denominator.

STEP 2

1. Simplify the expression by reducing the powers of x x .
2. Simplify the expression by reducing the powers of y y .
3. Write the simplified expression.

STEP 3

Simplify the powers of x x by subtracting the exponent in the denominator from the exponent in the numerator:
x18÷x5=x185=x13 x^{18} \div x^{5} = x^{18-5} = x^{13}

STEP 4

Simplify the powers of y y by subtracting the exponent in the denominator from the exponent in the numerator:
y20÷y7=y207=y13 y^{20} \div y^{7} = y^{20-7} = y^{13}

STEP 5

Combine the simplified terms to write the final simplified expression:
5x18y2037x5y7=5x13y1337 \frac{5 x^{18} y^{20}}{37 x^{5} y^{7}} = \frac{5 x^{13} y^{13}}{37}
The completely simplified expression is:
5x13y1337 \boxed{\frac{5 x^{13} y^{13}}{37}}

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