what is the numerical equivalent of 8^-3 the answer should not contain any decimals or exponent expression
The numerical equivalent of 8^-3 without decimals or exponent expression is 1/512.
To find the numerical equivalent of 8^-3 without decimals or exponent expressions, we can calculate it step-by-step.
Step 1: Calculate the reciprocal of 8 by flipping the fraction: 1/8.
Step 2: Cube the reciprocal of 8: (1/8)^3 = 1/512.
Step 3: Simplify the fraction by writing it as a division: 1 ÷ 512 = 1/512.
Therefore, the numerical equivalent of 8^-3 without decimals or exponent expressions is 1/512.
To find the numerical equivalent of 8 raised to the power of -3, we first need to understand the concept of a negative exponent.
When we have a positive exponent, it represents repeated multiplication. For example, 8^3 means 8 multiplied by itself three times: 8 x 8 x 8 = 512.
A negative exponent indicates division. Specifically, it means we should take the reciprocal or the multiplicative inverse of the base raised to the positive exponent. So, 8^-3 is equal to 1 divided by (8^3), or 1/512.
Since you mentioned that the answer should not contain any decimals or exponent expressions, we need to find a way to express 1/512 without such notation.
To convert a fraction to a whole number without decimals, you can multiply both the numerator and denominator by a suitable factor so that the denominator becomes 1.
In this case, multiplying 1/512 by 1000 will give us a denominator of 1000 (which is effectively multiplying by 1), resulting in a whole number.
1/512 * 1000/1000 = 1000/512
Now, we can simplify the fraction by finding the greatest common divisor (GCD) between the numerator and denominator, and then divide both by that GCD.
The GCD of 1000 and 512 is 8, so dividing both by 8 gives:
1000/8 = 125
Therefore, the numerical equivalent of 8^-3 without any decimals or exponent expression is 125.