Verify if (c²ba)/(bac) = 1/c: Fraction Simplification Challenge

Question

Indicate whether true or false

c2babac=1c \frac{c^2\cdot b\cdot a}{b\cdot a\cdot c}=\frac{1}{c}

Video Solution

Solution Steps

00:00 Determine if the equation is correct
00:05 Break down the exponent into multiplications
00:14 Simplify what we can
00:26 Compare the expressions, and we'll see they're opposite, therefore not equal
00:35 And this is the solution to the question

Step-by-Step Solution

To solve this problem, we'll focus on simplifying the fraction:

Given: c2babac \frac{c^2 \cdot b \cdot a}{b \cdot a \cdot c} .

Step 1: Identify and cancel common factors from the numerator and the denominator. Note that both the numerator and the denominator have b b , a a , and c c as common factors.

Step 2: Cancel b b and a a from both the numerator and the denominator to simplify:

c2babac=c2c \frac{c^2 \cdot b \cdot a}{b \cdot a \cdot c} = \frac{c^2}{c}

Step 3: Simplify the remaining expression by canceling c c from the numerator and denominator:

c2c=c \frac{c^2}{c} = c

The simplified expression is c c , not 1c \frac{1}{c} .

Therefore, the given statement that c2babac=1c \frac{c^2 \cdot b \cdot a}{b \cdot a \cdot c} = \frac{1}{c} is Not true.

Answer

Not true