Question

5^2 × 3^-4 × 15^5 × 5^-8


^ <---------this sign means raise to the power​

Answer 1

Answer:

${5}^{2} \times {3}^{ - 4} \times {15}^{5} \times {5}^{ - 8}$

Exponentiation: 5 ^ 2 = 25

Exponentiation: 3 ^ (-4) = 0.012345679012346 = 1/

81

Multiple: the result of step No. 1 * the result of step No. 2 = 25 * 1/

81

= 25 · 1/

1 · 81

= 25/

81

Multiply both numerators and denominators. Result fraction keep to lowest possible denominator GCD(25, 81) = 1. In the next intermediate step, the fraction result cannot be further simplified by canceling.

In words - twenty-five multiplied by one eighty-first = twenty-five eighty-firsts.

Exponentiation: 15 ^ 5 = 759375

Multiple: the result of step No. 3 * the result of step No. 4 = 25/

81

* 759375 = 25 · 759375/

81 · 1

= 18984375/

81

= 234375 · 81/

1 · 81

= 234375

Multiply both numerators and denominators. Result fraction keep to lowest possible denominator GCD(18984375, 81) = 81. In the next intermediate step, , cancel by a common factor of 81 gives 234375/

1

.

In words - twenty-five eighty-firsts multiplied by seven hundred fifty-nine thousand three hundred seventy-five = two hundred thirty-four thousand three hundred seventy-five.

Exponentiation: 5 ^ (-8) = 2.56E-6 = 1/

390625

Multiple: the result of step No. 5 * the result of step No. 6 = 234375 * 1/

390625

= 234375 · 1/

1 · 390625

= 234375/

390625

= 3 · 78125/

5 · 78125

= 3/

5

Multiply both numerators and denominators. Result fraction keep to lowest possible denominator GCD(234375, 390625) = 78125. In the next intermediate step, , cancel by a common factor of 78125 gives 3/

5

.

In words - two hundred thirty-four thousand three hundred seventy-five multiplied by one over three hundred ninety thousand six hundred twenty-five = three fifths.