Using laws of exponents, simplify - 3 4 × - 3 5 × - 3 2 and write the answers in exponential form.

The given expression is - 3 4 × - 3 5 × - 3 2 , We know the law of multiplying powers with the same base, For any non-zero rational number x and positive integers m and n , we have x m × x n = x m + n . By applying the law of exponent, we get, ⇒ - 3 4 × - 3 5 × - 3 2 = - 3 4 + 5 + 2 = - 3 11 Hence, the given expression in exponential form is - 3 11 .

Using laws of exponents, simplify - 3 4 × - 3 5 × - 3 2 and write the answers in exponential form.

The given expression is - 3 4 × - 3 5 × - 3 2 , We know the law of multiplying powers with the same base, For any non-zero rational number x and positive integers m and n , we have x m × x n = x m + n . By applying the law of exponent, we get, ⇒ - 3 4 × - 3 5 × - 3 2 = - 3 4 + 5 + 2 = - 3 11 Hence, the given expression in exponential form is - 3 11 .

Using laws of exponents, simplify a 5 × a 7 and write the answers in exponential form.

The given expression is a 5 × a 7 , We know the law of multiplying powers with the same base, For any non-zero rational number x and positive integers m and n , we have x m × x n = x m + n . By applying the law of exponent, we get, ⇒ a 5 × a 7 = a 5 + 7 = a 12 Hence, the given expression in exponential form is a 12 .

Using laws of exponents, simplify 2 12 ÷ 2 7 × 9 - 5 and write the answers in exponential form.

The given expression is 2 12 ÷ 2 7 × 9 - 5 , We know the law of exponent, for any non-zero rational number x and positive integers m and n , we have x m ÷ x n = x m - n when m > n . By applying the law of exponent, we get, ⇒ 2 12 ÷ 2 7 × 9 - 5 = 2 12 - 7 × 9 - 5 = 2 5 × 9 - 5 Also know that, x - m = 1 x m = 2 5 × 1 9 5 = 2 9 5 Hence, the given expression in exponential form is 2 9 5 .

Using laws of exponents, simplify 8 5 - 6 × - 5 8 - 2 and write the answers in exponential form.

The given expression is 8 5 - 6 × - 5 8 - 2 , We know that, for any non-zero integer a and an integer m , we can write a - m = 1 a m . So, 8 5 - 6 × - 5 8 - 2 = 8 5 - 6 × 1 - 5 8 2 = 8 5 - 6 × 8 5 2 Also know that, a m × a n = a m + n = 8 5 - 6 + 2 = 8 5 - 4 = 1 8 5 4 = 5 8 4 Hence, the given expression in exponential form is 5 8 4 .

Using laws of exponents, simplify 3 2 3 ÷ 6 3 2 and write the answers in exponential form.

The given expression is 3 2 3 ÷ 6 3 2 , We know the law of exponent, for any non-zero rational number x and positive integers m and n , we have x m n = x m n . By applying the law of exponent, we get, ⇒ 3 2 3 ÷ 6 3 2 = 3 6 ÷ 6 6 = 3 6 6 6 Also know that, x m ÷ y m = x y m = 3 6 6 = 1 2 6 = 1 2 6 Hence, the given expression in exponential form is 1 2 6 .

Using laws of exponents, simplify 4 3 4 ÷ 4 2 6 and write the answers in exponential form.

The given expression is 4 3 4 ÷ 4 2 6 , We know the law of exponent, for any non-zero rational number x and positive integers m and n , we have x m n = x m n . By applying the law of exponent, we get, ⇒ 4 3 4 ÷ 4 2 6 = 4 12 ÷ 4 12 = 4 12 4 12 Also know that, x m ÷ x n = x m - n = 4 12 - 12 = 4 0 = 1 ∵ x 0 = 1 Hence, the given expression in exponential form is 1 .

Simplify 2 5 × 3 5 and express each of the following in exponential form.

The given expression is 2 5 × 3 5 , We know the law of exponent, for any non-zero rational number x and positive integers m and n , we have x m × y m = x y m . By applying the law of exponent, we get, ⇒ 2 5 × 3 5 = 2 × 3 5 = 6 5 Hence, the given expression in exponential form is 6 5 .