Photo AI

14 (a) Find the value of x in each of the following - OCR - GCSE Maths - Question 14 - 2018 - Paper 1

Question 14

14 (a) Find the value of x in each of the following. (i) $\frac{a^4 \times a^3}{a^x} = a^x$ (ii) $\left( b^4 \right)^{3} = b^{k}$ (b) Factorise fully. $18x^2 ... show full transcript

Worked Solution & Example Answer:14 (a) Find the value of x in each of the following - OCR - GCSE Maths - Question 14 - 2018 - Paper 1

Step 1

(i) $\frac{a^4 \times a^3}{a^x} = a^x$

96%

114 rated

Answer

To solve for $x$ , we first simplify the left side:

Combine the exponents in the numerator: $a^4 \times a^3 = a^{4+3} = a^7$
Rewrite the equation: $\frac{a^7}{a^x} = a^x$
Apply the quotient rule for exponents: $a^{7-x} = a^x$
Since the bases are the same, we can set the exponents equal to each other: $7 - x = x$
Solve for x: $7 = 2x \implies x = \frac{7}{2}$ . Therefore, the value of $x$ is $\frac{7}{2}$ .

Step 2

(ii) $\left( b^4 \right)^{3} = b^{k}$

99%

104 rated

Answer

To find the value of $k$ , we simplify the left side:

Apply the power of a power rule: $\left( b^4 \right)^{3} = b^{4 \times 3} = b^{12}$
Therefore, we equate the exponents: $12 = k$

Thus, the value of $k$ is $12$ .

Step 3

Factorise fully. $18x^2 + 9x$

96%

101 rated

Answer

To factorise the expression $18x^2 + 9x$ fully, follow these steps:

Identify the greatest common factor (GCF) of the terms:
- The GCF of $18x^2$ and $9x$ is $9x$ .
Factor out the GCF: $18x^2 + 9x = 9x(2x + 1)$
Therefore, the fully factorised form is: $9x(2x + 1)$ .

Join the GCSE students using SimpleStudy...

97% of Students

Report Improved Results

98% of Students

Recommend to friends

100,000+

Students Supported

1 Million+

Questions answered

;