🧮 algebra

1. **State the problem:** We are given $Z = 2^5 \times 3^m \times 5^2$ and need to express $24Z$ as a product of powers of its prime factors. 2. **Express 24 as prime factors:**

1. The problem asks us to write the number $N = 33 \times 30$ as a product of its prime factors. 2. First, find the prime factorization of each number separately.

1. The problem asks us to write the number 126 as a product of its prime factors. 2. Start by finding the smallest prime number that divides 126. Since 126 is even, it is divisible

1. The problem asks us to write the number 28 as the product of its prime factors. 2. Start by finding the smallest prime number that divides 28. Since 28 is even, it is divisible

1. The problem asks us to write 124 as a product of its prime factors. 2. Start by dividing 124 by the smallest prime number 2: $$124 \div 2 = 62$$.

1. The problem asks us to write 140 as a product of its prime factors. 2. Start by finding the smallest prime number that divides 140. Since 140 is even, it is divisible by 2.

1. The problem asks to write the number 21 as the product of its prime factors. 2. Prime factorization means expressing a number as a product of prime numbers only.

1. **State the problem:** Find the prime factorisation of 44. 2. **Start with the smallest prime number:** 2. Check if 44 is divisible by 2.

1. **State the problem:** Fully factorise the expression $$18 - 6y + 15x$$ into single brackets. 2. **Identify common factors:** Look at each term: 18, -6y, and 15x. The coefficien

1. The problem asks us to write the number 825 as a product of its prime factors. 2. Start by finding the smallest prime number that divides 825. Since 825 ends with a 5, it is div

1. The problem asks us to write the number 22 as the product of its prime factors. 2. Prime factors are prime numbers that multiply together to give the original number.

1. The problem asks to find the missing prime factor in the factorization of 800 given as $$800 = 2 \times 2 \times 2 \times 2 \times 2 \times 5 \times \ldots$$ 2. First, calculate

1. The problem asks to find the value of a negative number raised to a positive power, specifically $-(9^2)$. 2. First, calculate the exponentiation inside the parentheses: $9^2 =

1. The problem asks for an expression for the area of a rectangle with height $4x$ and width $2x - 1$. 2. Recall that the area $A$ of a rectangle is given by the formula:

1. The problem is to add the fractions $-\frac{3}{11}$ and $\frac{5}{6}$. We need to find the sum and determine if the result is positive or negative. 2. To add fractions, first fi

1. State the problem: Calculate $$\sqrt{5 + 13}^2 \times (4 - \sqrt{16})$$ using the order of operations. 2. Simplify inside the square root: $$5 + 13 = 18$$, so the expression bec

1. **State the problem:** Simplify the expression by collecting like terms: $$a^2 + a^2 + a^2 + a$$. 2. **Identify like terms:** The terms $$a^2$$ are like terms because they have

1. The problem is to expand and simplify the expression $$(x + 2)(x - 1)$$. 2. Use the distributive property (also known as FOIL for binomials) to multiply each term in the first b

1. The problem asks us to calculate $7 + (-9)$. 2. Adding a negative number is the same as subtracting the positive value of that number. So, $7 + (-9)$ is the same as $7 - 9$.

1. The problem asks for an expression for the area of a trapezium with parallel sides labeled $3x - 3$ and $5x$, and height $3x$. 2. Recall the formula for the area of a trapezium:

1. The problem provides distances for three stages of a triathlon: Swim, Cycle, and Run, given in scientific notation. 2. We need to understand and possibly convert these distances