Evaluate (4/3)-3

Solution:

Given expression (4/3)^-3

According to the negative law of exponents, we have

a^-n = 1/aⁿ

So,  (4/3)^-3 = 1/( (4/3)³

(4/3)³ =  (4/3) × (4/3) × (4/3)

= (4 × 4 × 4)/(3 × 3 × 3) = 64/27

So, 1/( (4/3)³ = 1/(64/27)

= 27/64

Hence,

the value of (4/3)^-3 = 27/64.

In math, we use the terms “exponents and powers” when a number is multiplied by itself by a specific number of times. The number of times the number is multiplied by itself is equal to a number raised to the power of a natural number. For example, if a number “a” is multiplied by itself m times, then the expression obtained is defined as “a to the power of the m, or a raised to m”. Here, “a” is the base and “m” is the exponent. The base of an exponential expression refers to the number that is multiplied repeatedly by itself, while the exponent refers to the number of times the number is being multiplied. For example, 4 × 4 × 4 × 4 × 4 = 1024, where it can be written as 4⁵ in its exponential form. Here, 4⁵ means the number “4” is multiplied by itself by “5” times, “4” is the base number, and “5” is the exponent, and we read it as “4 raised to the power of 5”.

“a raised to the power of m”

a^m = a × a × a × a ×…….× a (m times)

“a” is the base of a^m

“m” is the exponent of a^m