Simplify the expression:
.1 square root a^6 where a<0
a^3 * a^3 = a^6
for example
a = -2
-2*-2*-2 = -8 = a^3
-8 * -8 = 64 =( -2)^6
since a<0, √a^6 = |a^3| = -a^3
√(-2)^6 = √64 = 8
To simplify the expression .1 square root a^6 when a<0, we can follow these steps:
Step 1: Rewrite the expression using fractional exponents.
The square root can be written as an exponent of 1/2. So, the expression becomes:
.1 * a^(6/2)
Step 2: Simplify the exponent.
We have a negative value for a, so we need to apply some rules of exponents. Since the exponent is an even number (6/2 = 3), we can remove the negative sign by taking the absolute value of a. Thus, the expression becomes:
.1 * |a^3|
Step 3: Evaluate the absolute value.
The absolute value of a^3 will always be positive, regardless of the value of a. So, the expression simplifies to:
.1 * a^3
Therefore, the simplified expression is .1a^3.